In an opening 45 minutes dominated by a pulsating Town side the hosts had to wait until the 24th minute to break the deadlock.
Alex Fisher grabbed his fourth of the season to continue his electric form before Sessi D’Almeida opened his account in green and white three minutes before the break to put Yeovil in a commanding position.
Never looking like throwing away their advantage, the Glovers kept Stevenage at bay to pick up another three points.
Coming into the clash unbeaten since the opening day of the season, Darren Way named an unchanged side for a third match in succession.
With D’Almeida passed fit to play after limping off in midweek, the green and whites were still unable to call upon Stuart Nelson (calf), Shaun Donnellan (thigh), James Bailey (knee), Rhys Browne (hamstring) and Francois Zoko (knee).
Although enjoying a monopoly on possession from the off, clear-cut chances were hard to come by in the opening exchanges with Wes McDonald and Omar Sowumni going close before the lively McDonald registered the games first shot on target 12 minutes in.
In a half full of positives, Town were dealt a blow early on, however, when Tom James was forced to leave the field through injury, being replaced by Uganda international Bevis Mugabi.
Not altering the pattern of the match, Town remained on top and Fisher soon added to his tally after incredible work from Alex Pattison.
The midfielder broke past the Boro line and steamed into the box before cleverly laying the ball off to Fisher who gave Paul Farman no chance with a composed finished.
Although a goal to the good, the Glovers were dealt a second injury blow when the virtually unplayable McDonald was forced off to the visitors’ relief, to be replaced by Jordan Green.
Despite losing a second man to injury the hosts continued to dominate and deservedly doubled their lead three minutes before half-time.
Good work on the right from substitute Green lead to the diminutive winger pulling the ball back for D’Almeida who lashed in a left-footed strike which almost broke the net in the process.
In a second half where chances were at a premium, the Glovers comfortably maintained their two-goal lead.
The visitors – clearly given stern words by manager Dino Maamria at the break – came out in determined manner after the restart but couldn’t force Nathan Baxter into more than a couple of routine saves.
With time ticking by and not wanting to surrender their unbeaten start to the campaign, the visitors looked to get back into the game and almost did through half-time substitute Alex Reid.
A corner for Boro fell to Reid on the edge of the box but his drive at goal was blocked by Nathan Baxter before the young stopper gathered to ease to danger.
Stevenage’s best chances were coming from set pieces and centre-back Scott Cuthbert rose highest to meet Joel Byrom’s corner but couldn’t manage to guide his header below Baxter’s crossbar.
After another relentless midfield performance, goal scorer D’Almeida was replaced by Jake Gray with a little under 20 minutes remaining, leaving the field to a standing ovation.
Comfortably holding Boro at arm’s length, any chance of a dramatic comeback from the visitors was ruled out with three minutes left to play when Michael Timlin received his second yellow and subsequent marching orders.
Gray almost grabbed his first of the season as Farman kept it to 2-0 before Baxter ensured a third straight cleansheet by getting down well to Danny Newton’s low drive.
Moving undefeated since the opening day of the season, Town picked up their first win at Huish Park to send the Glovers faithful home happy.
Yeovil Town: Baxter; James (Mugabi 16′), Sowunmi, Warren, Dickinson; Arquin, D’Almeida (Gray 71′), Pattison, McDonald (Green 35′); Jaiyesimi, Fisher.
Bookings: D’Almeida 43′, Baxter 85′
Subs not used: Phillips, Santos, Rogers, Henry.
Stevenage: Farman; Wildin, Cuthbert, Henry, Hunt; Timlin, Byrom, Ball (Sonupe 27′), Kennedy (Reid 46′), Revell, Guthrie (Newton 57′).
Bookings: Sonupe 37′, Timlin 60′, 87′ (shown red card), Reid 65′
Subs not used: Dieng, Ferry, Reid, Wilkinson, Nugent.